Method of detecting breaks in logging signals relating to a region of a medium

ABSTRACT

Method of detecting breaks in logging signals consisting of logs of different kinds recorded as a function of depth, of the type consisting in selecting a portion from each of the said logs in such a way that all the selected portions have a same depth interval in common, one of the selected portions being regarded as reference portion; selecting a parent wavelet function and constructing, from the said parent function, a family of wavelet analysis functions dependent on spatial frequency and on depth, the said method being characterized in that it furthermore consists in calculating, for each portion of log selected and for each depth datum, the absolute value of the mean gradient of the characteristic quantity of the wavelet transform for the various spatial analysis frequencies; selecting, for each portion of log processed, the peaks of the absolute value of the mean gradient of the characteristic quantity.

The present invention relates to a method of detecting breaks in loggingsignals relating to a region of a medium, the logging signals being madeup of logs of different kinds recorded for the said region as a functionof depth, and the application of this method to a depthwise readjustmentof the said logs.

In numerous fields, it is necessary to rapidly correlate two or morecurves representing the variations of a first quantity as a function ofa second quantity, for purposes of comparison, fitting, etc.

The curves to be compared may be of the same kind, that is to sayrepresent the variations of one and the same first quantity as afunction of one and the same second quantity, or of different kinds.They may for example be recordings of one and the same physicalphenomenon which are however shifted in time or space, or recordingsrelating to different physical phenomena or else recordings relating toone and the same physical phenomenon recorded for example by differentmethods so that their frequency content is different.

The correlations may be performed numerically. The result obtained isgenerally global and rather unreliable if no constraining assumptionsare made regarding the signals, the method then consisting in choosingbetween several autocorrelation peaks. The correlation can be performedvisually, by manually shifting one of the curves with respect to theother along the axis of the second quantity. In this way, optimalsimilitude is sought over one or more portions of the curve viasuccessive shifts. This method makes it possible to take account ofprior knowledge. It is this one which is commonly employed in geophysicsfor the depthwise or timewise adjusting of seismic horizons or for thecorrelating of recordings performed in a well and of seismic recordings.

The main drawback of such a method lies in the difficulty in comparingsignals of possibly very different shapes, for example if theirfrequency content is different.

A process for analysing a signal, termed the wavelet analysis process,is known which makes it possible to decompose the said signal as a sumof elementary wavelet functions Ψ_(a,b), which each vibrate as sinusoidsover a range whose position on an axis is linked to the parameter b andwhose width is linked to the parameter a (central frequency), and whichare very strongly damped outside this range. The decomposition of asignal with the aid of a family of these wavelets constitutes what isreferred to as a “time/frequency” analysis, since the first and mostcommon decompositions were performed on recordings of the variations ofa first quantity as a function of time (the second quantity). In thiscase, the dimension of the parameter b is that of a time and thedimension of the parameter a is the dimension of the inverse of a time,hence of a temporal frequency.

For further information regarding wavelet decomposition or“time/frequency” analyses, reference may be made to the article“L'analyse par ondelette” [Wavelet analysis] by Yves MEYER et al.,published in “Pour la Science” of September 1987, to the work “Wavelets”by J. N. COMBES et al. published by Springer-Veriag, or else to theinternational patent application published under No. WO 92/18941, whichdocuments are incorporated into the present application.

Several types of functions may be used, making it possible to definenumerous families of wavelets having different properties. The lattermay for example be gaussian, boxcar or triangular functions, real orcomplex functions, which may or may not be mutually orthogonal.Reference will be made to the above-cited article to ascertain theconstraints applicable to these various functions and to others in orderto generate wavelet families.

For a specified family of wavelets Ψ_(a,b), the “wavelet transform” intwo dimensions z and x, which is associated with a recording s(z) alongthe z axis, is defined as the sequence of coefficients C_(a,b) whicheach correspond to the integral of the product of the recording s(z) tobe analysed times the elementary analysis wavelet Ψ_(a,b) according tothe values of b along the z axis and the values of a along an x axis. Inthe case where complex wavelets have been chosen to perform thetime/frequency analysis of a recording or of a signal, it becomespossible to define the real part, the imaginary part, the modulus orelse the phase of the wavelet transform. The coefficients C_(a,b) arecalculated through the well known formula:

C_(a,b)=∫_(−oo) ^(+oo)S(z)_(a,b)(z)dz

Methods and devices for identifying geological structures using wavelettransforms are described in particular in patents U.S. Pat. No.5,673,191, U.S. Pat. No. 5,740,036 and U.S. Pat. No. 5,757,309 and inthe article entitled “Detection of non stationarites in geological timeseries: wavelet transform of chaotic and cyclic sequences”, by AndreasPROKOPH et al, published in Computers and Geosciences, Vol. 22, N° 10,pages 1097-1108, 1996.

However, these latter documents relate either to magnetic andgravitational measurements for distinguishing between relatively deepgeological structures and shallow structures, or to means for simulatingthe succession of structures.

The present invention relates to a method of detecting breaks in loggingsignals, which uses a wavelet analysis of the said signals.

It is known that the analysis of the logging signals obtained with theaid of well known devices makes it possible to determine the mineralogy,the texture, the type of porous lattice and the fluid content of theformations through which boreholes are drilled. The depthwisealterations in the signals reflect the alterations in the properties ofthe formations and make it possible to chart their structural anddiagenetic sedimentary history.

Within the logging signals it is possible to distinguish breaks whichcorrespond to significant modifications of the nature of the formationswhich occur over a small depth interval.

Electrofaciological beds may be characterized on the basic of the breaksplotted on at least one of the channels of the logging signal. Inside abed, each channel of the logging signal shows a continuous variation, ona given depth resolution scale. The noteworthy breaks are used by thegeologist for lithostratigraphic correlation purposes. In certain cases,chronostratigraphic correlations are possible by performing aninterpretation on the basis of a conceptual model of the alterations ofthe sedimentary deposits.

Specialists performing the analysis of the logging signals use thenoteworthy breaks, in the first step of the interpretation, for thedepthwise readjustment of the various signals recorded by the sensors ofthe logging device which are not all located in front of the sameformation at the same time. On either side of the breaks, the loggingsignal suffers from a shoulder effect over an interval which depends onthe resolution of the logging devices and on the contrast of thecharacteristic logging responses of the formations. This shoulder effectis a source of errors and uncertainty in the interpretations.

The present-day processes for interpreting logging signals are based onprocessing each sample of the logging signal independently of thesamples lying above and below the processed sample, the concept of depthnot being involved. Accordingly, the information carried by thealterations of the signal with depth is not taken into account. In orderfor this information to be taken into account, it is necessary to definebreaks over the logging signal and alterations inside the breaks.

The determination of breaks is currently performed manually and requiresan experienced operator. The result is both subjective and difficult toreproduce identically. However, these breaks which correspond to thelimits of beds or of formations are necessary for depthwisereadjustment.

Depthwise readjustment is a fundamental step in all interpretation oflogs, since it consists in resetting to the same depth measurementsperformed by the various sensors of the logging devices, which do notpass simultaneously in front of the same point of the well.

Two types of readjustments are distinguished:

“intra run” readjustments, which relate to measurements recorded duringthe same ascent of a set of mechanically interlinked sensors;

“between runs” readjustments, which are facilitated by always recordinga common log in the various runs, this common log generally being the“gamma ray” log which serves as depth reference.

A first readjustment is performed at the time of acquisition and relatesonly to the measurements performed during the same recording. It issatisfactory only in the best cases and always has to be checked.

There are in existence stations for analysing logs and with the aid ofwhich it is possible to make readjustments. However, the readjustmentoperations remain manual or, when they are automatic, they relate onlyto logs of the same kind, the analysis stations being unableautomatically to analyse logs of different kinds. Therefore, onlyreadjustments between runs are possible. Moreover, the currentprocesses, based on correlations, do not make it possible to identify,hierarchize and assign a quality index to the correlations.

The aim of the present invention is to propose a method which makes itpossible automatically to detect breaks in logging signals or logs andwhich is able to be applied in respect of depthwise readjustment of thelogs recorded.

The subject of the present invention is a method of detecting breaks inlogging signals relating to a region of a medium and consisting of logsof different kinds recorded for the said region as a function of depth,of the type consisting in:

selecting a portion from each of the said logs in such a way that allthe selected portions have a same depth interval in common, one of theselected portions being regarded as reference portion,

determining a sequence of spatial analysis frequencies,

selecting a parent wavelet function and constructing, from the saidparent function, a family of wavelet analysis functions dependent onspatial frequency (or wavenumber) and on depth,

calculating a wavelet transform of the selected portion of each log andfor each analysis frequency,

choosing a characteristic quantity of the wavelet transform and in usingthis quantity as a representation of the wavelet transform, the saidmethod being characterized in that it furthermore consists in:

calculating, for each portion of log selected and for each depth datum,the absolute value of the mean gradient of the characteristic quantityof the wavelet transform for the various analysis frequencies,

selecting, for each portion of log processed, the peaks of the absolutevalue of the mean gradient of the characteristic quantity, each peakcorresponding to a break,

determining the corresponding breaks over the reference log portion,

defining an analysis window centred on each break of the reference logportion, and

selecting the breaks of the other log portions which lie in the analysiswindow.

An advantage of the present invention lies in the fact that all thecurves representative of the various logs recorded are taken intoaccount and processed rapidly (simultaneously or sequentially one afteranother).

Moreover, the method according to the invention makes it possible tocircumvent the shoulder effects linked with the resolution(effectiveness) of the logging devices so as to chop the intervalssupplying the logs into beds and to be able to analyse the verticalalterations in their various geological characteristics.

According to another characteristic, the result of the wavelet transformis a complex number and the characteristic quantity of the wavelettransform is the real part of the said complex number. The parentfunction may for example be a function of the type f(z)=(1−z²)exp(−z²/2).

According to another characteristic, the absolute value of the meangradient is normalized, the peaks of the absolute value of the meangradient which are selected are greater than or equal to a predeterminedthreshold. In particular, the absolute value of the mean gradient isnormalized and the threshold for selecting the peaks is equal to orgreater than 0.2.

According to another characteristic, the log supplying the referenceportion is obtained by gamma ray logging, the said (gamma ray) log beingan excellent depth reference since it can be recorded in all types ofdrilling mud and even through a casing.

According to another characteristic, each processed portion of log isincluded within an interval of study containing a predetermined numberof samples N. In particular, when the number of samples to be processedin a log portion is either less than or greater than the number ofsamples N of the interval of study, the log is either centred in thesaid interval and the empty parts of the latter are filled with sampleshaving a value equal to the mean value of the log, or else it is dividedinto at least two parts each comprising a number of samples less than N,in such a way as to process each part as indicated above.

According to another characteristic, the succession of the spatialanalysis frequencies used for the calculation of the wavelet transformhas as limits a frequency corresponding to a wavelength of 4 m and afrequency corresponding to a wavelength of 200 m. The succession of thesaid frequencies is for example a geometric progression. Preferably, tenspatial frequencies are selected, the limits of which correspond towavelengths of 10 m and 100 m.

Each spatial frequency is analysed independently of the others, withoutsuccessive filtering. Moreover, choosing the frequencies makes itpossible to have a number of wavelet coefficients which is sufficient tocarry out a study of their spatial organization, in the depth/frequencyplane. In this way, three-dimensional information is obtained linkingthe depth, the frequencies present in the starting logging signal andthe amplitude of the transform.

Thus, the method according to the invention makes it possible to study,for each depth datum, the logging signal at various scales, that is tosay over depth intervals whose size differs.

The method according to the invention makes it possible to hierarchizethe breaks according to various logging criteria and to give priorities(or quality criteria) in the references which are used in particular inthe depth readjustment. Thus, it is possible automatically to processboth an “intra run” readjustment and a “between runs” readjustment.

Other advantages and characteristics will be better apparent fromreading a preferred embodiment of the method according to the invention,as well as of the appended drawings in which:

FIG. 1 is a representation of the breaks over a set of non-readjustedlogs, comprising a gamma ray log as reference;

FIG. 2 is a representation of the real part of the coefficients of thewavelet transform of the reference log;

FIG. 3 is a representation of the gradient of the real part of thecoefficients of the wavelet transform of the reference log;

FIG. 4 is a representation of the absolute value of the normalized meangradient for the reference log.

For a given medium to be explored, various logs are recorded as afunction of depth and correspond to a region of the said medium. In theexample of FIG. 1, six logs referenced 1 to 6 have been recorded. Log 1is obtained by gamma ray logging and constitutes a gamma ray log; log 2corresponds to a recording representing the hydrogen index and it isusually referenced NPHI. Log 3 corresponds to the density of the rock inplace in the relevant region, and it is referenced RHOB; log 4corresponds to the slowness Dt in the said relevant region; logs 5 and 6correspond to resistivities designated by LLS to represent the shallowresistivity and by LLD to represent the deep resistivity.

In each log 1 to 6 a portion is selected which relates to the same depthinterval, then from these log portions is chosen a portion which is usedas reference portion. In the example represented in FIG. 1, thereference portion is that of the gamma ray.

In another step, a parent wavelet function is selected, for example theMORLET wavelet function or better still the function referred to as the“Mexican hat” wavelet function, of the type f(z)=(1−z²)exp (−z²/2) whichis equivalent to a “gaussian” smoothing whose second derivative istaken. A family of analysis functions which depends on spatial frequencyand on depth is constructed from the parent wavelet function, as isknown and recalled above. In the present case, ten analysis frequenciesare chosen, the limits of which lie between a frequency F₁ correspondingto a wavelength λ of 10 m and a frequency F₁₀ corresponding to awavelength of around 100 m, the succession of analysis frequencies F₁ toF₁₀ decreasing in accordance with a geometric progression, of commonratio 1.24 for example.

Each log 1 to 6 or rather each selected portion of log is thus processedwith the aid of the wavelet transform, doing so for each analysisfrequency.

The result of the wavelet transform is a coefficient represented by acomplex number, only the real part of which is preserved ascharacteristic quantity. FIG. 2 represents the real part of thecoefficients of the wavelet transform for the reference portion of thegamma ray log, the values increasing from left to right. The columnsituated immediately after the gamma ray log 1 in FIG. 2 corresponds tothe real part of the coefficients of the wavelet transform for the firstfrequency F₁, the next column corresponding to the real part of thecoefficients of the wavelet transform for the frequency F₂, and so onand so forth on moving to the right up to the frequency F₁₀.

For each datum of each log portion analysed, the absolute value of themean gradient of the real part of the complex number of the result ofthe wavelet transform is calculated. In FIG. 3, the gradient of the realpart of the coefficients of the wavelet transform has been representedfor the reference portion selected in the gamma ray, as with regard toFIG. 2. Thus, the column following the gamma ray situated furthest tothe left, alongside the depth scale in metres, corresponds to thegradient of the real part represented in FIG. 2 and corresponding to theinitial frequency F₁. To each frequency F₂, F₃ . . . F₁₀ therecorresponds a gradient of the real part.

We proceed likewise for each of the logs 2 to 6, that is to say each logis processed with the aid of the family of wavelet analysis functionsemanating from the name parent wavelet function, in such a way that toeach log there corresponds a representation of the gradient of the realpart of the wavelet transform for each of the analysis frequencies F₁ toF₁₀.

In another step, the absolute value of the mean gradient of the realpart chosen as characteristic quantity of the wavelet transform iscalculated for each portion of log selected and for each depth datum, onthe basis of the absolute values of the gradients determined for the setof analysis frequencies F₁ to F₁₀. By referring to FIG. 3 and for eachdepth datum, for example the death datum 1613, the mean gradient iscalculated by taking, for example, the arithmetic mean of the values ofthe gradient for each datum and for each of the frequencies F₁ to F₁₀.Next, for each portion of log selected, the peaks of the absolute valueof the mean gradient are selected. In FIG. 4, representing thenormalized mean gradient which corresponds to the gamma ray log alone,it may be seen that between 1610 and 1623 m, the mean gradient for eachdepth datum lying between 1610 and 1623 m is relatively small, the firstpeak appearing for the datum 1623 m. Gradually, it is observed thatthere is a significant peak for the datum 1625 m, other peaks at 1638 m,1650 m, 1653 m and so on. To each value of the mean gradient therecorresponds a sought-after break.

Preferably, and for each depth datum, only the peaks of the absolutevalue of the mean gradient which are greater than a predeterminedthreshold are selected. For example, the absolute value of the meangradient is normalized and only the peaks greater than the threshold 0.2are retained.

FIG. 1 supplies, alongside each portion 1 to 6 of log selected, arepresentation of the peaks selected for each depth datum and thereforeof the breaks which have been determined by virtue of the presentinvention. The sequence of breaks in the column referenced 1′corresponds to the series of peaks greater than 0.2, for the gamma raylog portion. As may be observed, for the interval of depth represented,a break has been determined for the datum 1623, another for the datum1625 m, another for the datum 1626 m and so on. Column 2′ represents theseries of breaks determined for the NPHI log portion, column 3′representing the series of breaks determined for the RHOB log portionand so on.

For reasons of clarity and compactness, the portions of log selected liebetween the depth datum 1610 m and the depth datum 1679 m. In realityand preferably, the log portions selected are included within aninterval of study which comprises a given number N of logging samples,for example 4096 samples. If a sampling spacing of 15.24 cm (½ a foot)is considered, this represents a length of log of 624 metres instead ofthe 69 metres indicated in FIGS. 1 to 3.

As indicated previously, N samples are processed in each portion of logselected.

When the portion of log to be processed comprises fewer than the fixednumber N of samples, 4096 in the present case, the portion of log isrecentred in the set of 4096 samples. For example, if the portion of logselected comprises 2000 samples, a log of 4096 samples is created, ofwhich the first 1048 and the last 1048 are assigned the mean value ofthe log, the other 2000 samples corresponding to the original log.

When the portion of log selected comprises more samples that the fixednumber N, for example greater than 4096, the said portion is cut intotwo and each half is processed as if it contained fewer than 4096samples, in the manner indicated above.

According to the invention, it is preferable to search for the relevantbreaks in each log. To this end, a relevance window is defined which iscentred in succession on each break of the log under consideration, andfor each position of the said relevance window a relevance coefficientis calculated, defined by the expression:

(log_(max)−log_(min))window/log_(max)−log_(min))portion

in which:

log_(max) and log_(min) in the window represent the maximum and minimumamplitudes of the logging signal situated in the window,

log_(max) and log_(min) in the portion of log processed represent themaximum and minimum amplitudes of the processed portion of the loggingsignal.

Such an operation contributes to eliminating the problems linked tonoise in the logging signals recorded.

For each log, only the breaks for which the relevance coefficient isgreater than a given value are retained. Columns 1′ to 6′ represent thebreaks retained with the aid of the above calculation for logs 1 to 6respectively.

So as to retain or select only the interesting breaks which correspondfrom one log to another, the present invention advocates that the breaksretained on each of the portions of log selected be hierarchized. To dothis, an analysis window is defined which covers a given number M ofsamples, equal to 5 for example. For each break of the reference log,the analysis window is centred on this break and the other logs aresearched in order to find the breaks which are situated in the saidwindow. Each break determined on one or more logs, in the window underconsideration, is associated with the break of the reference log onwhich the window was centred. After this, the breaks can be mutuallyhierarchized, by operating for example as follows.

In the columns of the breaks, it may be seen that a break determined forthe datum 1623 m in column 1′ is also present only in column 4′ andabsent from the other columns 2′, 3′, 5 and 6′. Since it is present onlyin one column 4′ other than the reference column 1′, the coefficient oneis assigned to it. The break determined at around 1626 m in column 1′ ispresent in columns 2′, 3′, 5′ and 6′; the coefficient four is assignedto it. The break determined at 1631 m in column 1′ is also present ineach of the other columns 2′ to 6′: the coefficient five is assigned toit and this operation is repeated for each of the breaks of the column1′. The hierarchization is represented in column 7′ of FIG. 1. In thiscolumn 7′, it may be observed that there are four breaks having thecoefficient 5, five breaks having the coefficient four, and so on.

Because they correspond to noteworthy geological events, breaks are usedfor depthwise readjustment of logs. A depth readjustment of logsconsists in resetting to the same depth measurements performed byvarious sensors which do not pass simultaneously in front of the samepoint of the well. To perform an automatic depthwise readjustment,breaks are detected on each log, in the manner indicated above.Likewise, a search is made for the breaks existing on the other logsvisible in a depth window centred on each break plotted on the referencelog. When a break is detected on one or more logs, it is associated withthe break detected on the reference log. The values of the logs arerecalculated in such a way that the breaks associated with each of thebreaks of the reference log appear at the same depth datum as therelevant break of the reference log.

What is claimed is:
 1. Method of detecting breaks in logging signalsrelating to a region of a medium and consisting of logs of differentkinds recorded for the said region as a function of depth, of the typeconsisting in: selecting a portion from each of the said logs in such away that all the selected portions have a same depth interval in common,one of the selected portions being regarded as reference portion,determining a sequence of spatial analysis frequencies, selecting aparent wavelet function and constructing, from the said parent function,a family of wavelet analysis functions dependent on spatial frequencyand on depth, calculating a wavelet transform of the selected portion ofeach log and for each spatial analysis frequency, choosing acharacteristic quantity of the wavelet transform and in using thisquantity as a representation of the wavelet transform, the said methodbeing characterized in that it furthermore consists in: calculating, foreach portion of log selected and for each depth datum, the absolutevalue of the mean gradient of the characteristic quantity of the wavelettransform for the various spatial analysis frequencies, selecting, foreach portion of log processed, the peaks of the absolute value of themean gradient of the characteristic quantity, each peak corresponding toa break, determining the corresponding breaks over the reference logportion, defining an analysis window centred on each break of thereference log portion, and selecting the breaks of the other logportions which lie in the analysis window.
 2. Method according to claim1, characterized in that the result of the wavelet transform is acomplex number and in that the Characteristic quantity of the wavelettransform is the real part of the said complex number.
 3. Methodaccording to claim 1, characterized in that the selected peaks of theabsolute value of the mean gradient are greater than or equal to apredetermined threshold.
 4. Method according to claim 3, characterizedin that the absolute value of the mean gradient is normalized and inthat the said threshold is greater than or equal to 0.2.
 5. Methodaccording to claim 1, characterized in that the log supplying thereference portion is a log obtained by gamma ray logging.
 6. Methodaccording to claim 1, characterized in that each portion of log isincluded within an interval of study containing a predetermined numberof samples N.
 7. Method according to claim 6, characterized in that whena log intended to supply a selected portion is made up of a number ofsamples which is less than the number N, the said log is centred in theinterval of study and the empty parts of the said interval are filledwith samples having a value equal to the mean value of the log. 8.Method according to claim 6, characterized in that when a log intendedto supply a selected portion is made up of a number of samples which isgreater than the number N, the said log is divided into at least twoparts each having a number of samples less than the number N.
 9. Methodaccording to claim 1, characterized in that the spatial analysisfrequencies selected for the calculation of the wavelet transform havelimit frequencies corresponding to a wavelength of 4 m and to awavelength of 200 m.
 10. Method according to claim 9, characterized inthat ten spatial frequencies are selected, the limit frequencies ofwhich correspond to wavelengths of 10 m and 100 m.
 11. Method accordingto claim 9, characterized in that the succession of spatial analysisfrequencies is a geometric progression.
 12. Method according to claim 1,characterized in that the parent wavelet function is a function of thetype f(z)=(1−Z²)exp (−z²/2) in which z is the depth.
 13. Method ofdepthwise readjustment of logs of different kinds recorded for a regionof a medium as a function of depth, characterized in that it consists indetermining breaks over a log portion chosen as reference and overcorresponding portions of the other logs by applying the methodaccording to claim 1 and in recalculating the values of the said otherportions of log in such a way that the breaks of the said portions,which are associated with each of the breaks of the log portion chosenas reference, appear at the same depth datum as the relevant break ofthe reference log.